[This is the second time I've sent this because the first did not seem to go
through. My apologies if you got this twice.]
I don't want to put words in his mouth, but Robert Cohen seems to be
thinking along the same lines as I am. It strikes us as inappropriate to
apply R = V/I to some objects like batteries, capacitors, inductors. He
says, "in my mind, it is the 'cause or 'reason' why the current is
impeded..."
That's what I've been trying to say all along. I would probably reword his
statement say "We have to determine why the device has a potential
difference across it." A battery has a potential difference across it
because of an electrochemical reaction, not because of I*R. A capacitor has
a potential difference across it because V = Q/C, not because if I*R. A
reverse-biased zener diode has a potential difference across it because the
potential difference is required to get breakdown and obtain charge carriers
at the junction, not because of I*R. Whether you use Robert's words or
mine, the conclusion is the same... don't calculate a resistance for these
devices using R = V/I... it is inappropriate to assign a resistance to these
devices.
On this basis, I fully agree with Robert that it is appropriate to assign a
resistance to a light bulb. I've tried to say that all along. The
potential difference across an operating light bulb is due to I*R where R
can be calculated by rho*L/A where rho is the resistivity, and rho is
temperature dependent. This is the same as we would do for any resistor.
It is from this train of thought that I declared light bulbs follow Ohm's
Law if regular resistors do, because they behave similarly... the light bulb
merely has a greater temperature difference when we vary its operating
parameters compared to when we vary the operating parameters of a regular
resistor. The mechanism of impeding the current (Cohen's words) or the
mechanism of generating the potential difference (my words) is the same for
a light bulb and a nichrome resistor.
Mark Sylvester is also asking some good questions about dissipation. Can we
say something has resistance if "it is just sitting there dissipating?"
It's a good question, but I think the answer is no. We also calculate the
heat dissipation for a reverse-biased zener diode as I*V where I is the
current through it, and the V is the potential difference across it. But,
as mentioned above, I do not regard the zener diode as having a resistance
because the potential difference across it is not calculated by I*R. So the
zener diode is one of several examples where the idea of dissipation does
not help us.
Aside.... Sometimes I find it helpful to speak in terms of active versus
passive circuit elements, where active devices can supply energy to the
circuit and passive devices take energy from the circuit. This is most
useful when trying to put +/- signs on device terminals once you know which
way the current goes through it, or once you know it is supplying or
receiving energy. This can get really confusing when looking at things like
transistors because they are often considered active in conjunction with the
power supply that is biasing the collector/emitter circuit. The only point
in bringing this active/passive stuff up is to say that I do not believe it
helps the present discussion. That is, I am trying to reinforce that I
don't think Mark's idea of "sitting there dissipating" is going to resolve
this issue.
As Leigh is telling us, I don't view R = V/I as any sort of physical law. I
view it as a useful relation in some cases. Those cases for which I believe
it is relevant are those cases where R can also be calculated by rho*L/A.
Or I might also say it is relevant for cases where V = I*R, but that will
strike some as circular reasoning.
I certainly agree with Mark that this can be a "pedagogical nightmare."
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817